Question

In an isosceles triangle, if the vertex angle is twice the sum of the base angles calculate the angles of the triangle.

Answer 1

Let us assume that the base angle of the isosceles triangle, then the vertex angle will be 2ao. As we know that the sum of three angles of a triangle equal to 180o. Since the base angles are equal, then the base angles are 45o each, the vertex angle will be 2 x 45o = 90.

Answer 2

so according to ur question the vertex angle is twice the sum of the base angles so, take one base angle as x

u know that the base triangles of an isosceles triangle is always equal

so we found the 2 base angles that is = x

now the sum = x + x = 2x ( this is the sum of the base angles )

now we need to find the other angle 

the other angle is twice the sum of the sum of the 2 base angles = 2 * 2x = 4x

now we can calculate the angles

4x + 2x = 1800  ( angle sum property of a triangle )

6x = 180

x = 180 / 6 = 30

therfore the base angles are 300 and 300 and the vertex angle = 2 * ( 30 + 30 ) = 2 * 60 = 1200